IB Math Studies Functions

1. IB Mathematical Studies SL – Functions, simplest form

How can I find in simplest form ,where .

Solution

IB Mathematical Studies SL – Functions, simplest form

The functions in simplest form are:

2. IB Mathematical Studies SL – Linear Functions

How can we find a formula that describes the cost of running a car if there is a standard cost of $100 plus$0.1 per one kilometer thereafter?

Solution

IB Mathematical Studies SL – Linear Functions

Let x be the kilometers then the linear function that describes the above word problem is:

3. IB Mathematical Studies SL – Quadratic Functions

The profit of a PC manufacturer company of making x personal computers (PC) per day is given by the following formula:

How can we find the profit in dollars in the following cases:

for 10 PCs, 40PCs and 100PCs

Solution

IB Mathematical Studies SL – Quadratic Functions

The profit of the company when being produced 10 PCs is given by

The profit of the company when being produced 40 PCs is given

The profit of the company when it  produces 100 PCs is given

4. IB Mathematical Studies SL – Complete the square

How can we complete the square and find the vertex of the following quadratic function:

Solution

IB Mathematical Studies SL – Complete the square

Completing the square is a procedure for reformatting quadratic functions.

Quadratic Functions of the form can be rewritten as

The major reason for doing this is that it allows us to easily see the vertex of the curve which is located at the point .

The general method of completing the square can be shown like this:

Therefore the x-coordinate of the vertex is

Concerning this question if we follow the preceding procedure we have:

Therefore the coordinates of the vertex are

5. IB Mathematical Studies SL – Factorisation

How can we factorize this expression ?

Solution

IB Mathematical Studies SL – Factorization, difference of squares

We‘ll use the difference of squares identity

Concerning this question the factorization is

6. IB Mathematical Studies SL – Factorisation, Common Factor

How can we fully factorize the following expression:

?

Solution

IB Mathematical Studies SL – Factorisation, common factor

The expression can be factorized as follows

?